A thermomechanical framework for constitutive models for rate-independent dissipative materials

A formulation of elastic-plastic theory for rate independent materials is d escribed, based on the use of thermodynamic potentials. The four energy fun ctions commonly used in thermodynamics (internal energy, Helmholtz free ene rgy, enthalpy and Gibbs free energy) are used to provide descriptions depen ding on which combinations of the stress, strain, temperature and entropy a re taken as the independent variables. Much use is made of Legendre transfo rmations to establish the links between the different energy functions. Dis sipative behaviour is introduced through the use of kinematic internal para meters, and their conjugate variables, which are termed generalised stresse s. A dissipation function or a yield function is used to describe the irrev ersible behaviour, and these are related by a degenerate case of the Legend re transformation. A central theme is that the constitutive behaviour is en tirely determined by the knowledge of two scalar potentials. A systematic p resentation is made of 16 possible ways of formulating constitutive behavio ur within this framework. From four of these forms it is possible to establ ish the incremental response entirely by differentiation of the two potenti als and by standard matrix manipulation. Examples are provided of the forms of the potentials for certain simple cases. The paper builds on previous w ork by Ziegler and other authors, and extends and generalises work by Colli ns and Houlsby to include thermal effects. (C) 2000 Elsevier Science Ltd. A ll rights reserved.